Constructionism in Practice: Designing, Thinking, and Learning in a Digital World

By Yasmin Kafai; Mitchel Resnick | Go to book overview
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tate greater conceptual understanding. The computer's capacity to repeat and vary large numbers of trials, as well as its ability to show the results of these trials in compressed time (and often in visual form), makes it possible to encapsulate events that are usually distributed over time and space. This can provide learners with the kinds of concrete experiences they need to build solid probabilistic intuitions.A central issue, then, is between learners using prebuilt models and learners making their own models. The ability to run prebuilt models interactively is an improvement over static textbook based approaches. By manipulating parameters of the model, users can make useful distinctions and test out some conjectures. The results of the Connected Probability project suggest that for learners to make use of these prebuilt models, they must first build their own models and design their own investigations.It is possible to combine the two approaches (e.g., Eisenberg, 1991; Wilensky, 1995, in preparation-b) by providing prebuilt models that are embedded in programming environments, creating so-called "extensible applications" ( Eisenberg, 1991). This combined approach has the advantages of both prebuilt and buildable models. The challenge of such an approach is to design the right middle level of primitives so that they are neither (a) too low-level so that the application becomes identical to its programming language, nor (b) too high-level so that the application turns into an exercise of running preconceived experiments. The metric by which the optimal level can be judged is in the usefulness to learners. This requires an extensive research program. The findings from this research must inform the development of modeling languages and their embedded extensible applications.
CONCLUDING REMARKS
In the Connected Probability project, learners such as Ellie succeeded in making deep probabilistic arguments that probed at the foundations of the discipline. Having understood the foundational concepts in this deep way, they developed a strong intuitive understanding of such concepts as randomness, distribution, and expectation. Solid intuitions about probability and statistics were clearly developed by learners in this study. This shows that we are not, by our natures, as some have argued, unable to reason intuitively about probability.The Connected Probability project is an instantiation of the Connected Mathematics approach. The key elements of the Connected Mathematics approach that enabled these changes are
The explorations of multiple meanings of concepts and making connections between these different representations.

Like Ellie, they saw the connections between representations of randomness

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Constructionism in Practice: Designing, Thinking, and Learning in a Digital World
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